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MONOMIAL AND MONOLITHIC CHARACTERS OF FINITE SOLVABLE GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  05 October 2021

BURCU ÇINARCI Open the ORCID record for BURCU ÇINARCI [Opens in a new window]
BURCU ÇINARCI*
Affiliation:
Maritime Faculty, Department of Marine Engineering, Piri Reis University, Istanbul 34940, Turkey
*
e-mail: burcu-cinarci@hotmail.com
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Abstract

Let G be a finite solvable group and let p be a prime divisor of $|G|$ . We prove that if every monomial monolithic character degree of G is divisible by p, then G has a normal p-complement and, if p is relatively prime to every monomial monolithic character degree of G, then G has a normal Sylow p-subgroup. We also classify all finite solvable groups having a unique imprimitive monolithic character.

Keywords

solvable groupmonolithic charactermonomial characterprimitive character

MSC classification

Primary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 440 - 448
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

The work of the author was supported by the Scientific Research Projects Coordination Unit of Piri Reis University (project number BAP-2020-004).

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